Lens array and image projection device

ABSTRACT

There is provided a lens array and an lens array capable of suitably preventing irregular brightness without reducing resolution. A micro lens array of a screen includes upper-level microlenses and lower-level microlenses which are formed on the incidence surface of the screen, which have the same effective diameter, and which have a structure that generates an optical path length difference Δ in transmission light. By disposing the upper-level microlenses and the lower-level microlenses at an interval based on the effective diameter, the basic periodic structure of a lens period is formed. Further, the upper-level microlenses and the lower-level microlenses form a basic block comprising a combination of the lenses having a structure that generates the optical path length difference. A concave-and-convex period PC based on the basic block is an integer multiple of the lens period.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional of U.S. patent application Ser. No.15/555,473, filed on Sep. 1, 2017, which is the U.S. National Phaseunder 35 U.S.C. § 371 of International Application No.PCT/JP2015/056311, filed on Mar. 4, 2015, the entire contents of eachare hereby incorporated by reference.

TECHNICAL FIELD

The present invention relates to a display system including a lens arraycapable of improving visibility.

BACKGROUND TECHNIQUE

Conventionally, there is proposed a technique for applying atransmission-type screen equipped with a microlens array to a head-updisplay and a laser projector. Using such a transmission-type screen ismore preferable than using a diffuser panel because an influence causedby the speckle noise can be suppressed. For example, in PatentReference-1, there is proposed an image forming device including a laserprojector and a microlens array on which plural microlenses arearranged. In Patent Reference-2, there is proposed a technique ofdetermining the pitch of each microlens so that the width of thediffraction of beam diffused by each microlens of a microlens array isequal to or shorter than the pupil diameter of the observer thereby toprevent the irregular brightness due to the uncertainty that the peak ofthe diffracted light diffused at the microlens enters the pupils of anobserver.

PRIOR ART REFERENCE Patent Reference

Patent Reference-1: Japanese Patent Application Laid-open under No.2010-145745

Patent Reference-2: Japanese Patent Application Laid-open under No.2013-064985

DISCLOSURE OF INVENTION Problem to be Solved by the Invention

When a lens array is used for a head-up display as an element forgenerating an intermediate image, determining a small pitch of the lensarray could lead to irregular brightness whereas determining a largepitch of the lens array could lead to the resolution degradation. PatentReference-1 does not disclose how to suppress the irregular brightness.In contrast, according to Patent Reference-2, since the pitch of thelens array is expanded, the resolution of the intermediate imagegenerated at the lens array deteriorates.

The present invention has been achieved in order to solve the aboveproblem. It is an object of the present invention to provide a lensarray and an image projection device capable of suitably suppress theirregular brightness without deteriorating the resolution.

Means for Solving the Problem

One invention is a lens array including plural lenses configured to havethe same effective diameter and to have a structure that generates anoptical path length difference in transmission light or reflectivelight, wherein each of the plural lenses is arranged at an intervalbased on the effective diameter thereby to form a two-dimensional basicperiodic structure, wherein a part of the plural lenses form a basicblock which is a combination of lenses having the structure thatgenerates the optical path length difference, wherein the basic block isrepeatedly arranged to form a two-dimensional secondary periodicstructure whose period is longer than the period of the basic periodicstructure, and wherein the period of the secondary periodic structure isan integer multiple of the period of the basic periodic structure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B illustrate schematic configurations of head-up displays.

FIG. 2 illustrates a side view of a screen in the Y-Z plane.

FIGS. 3A to 3C illustrate a configuration of a microlens array.

FIGS. 4A to 4E illustrate diffracted lights of the screen on the Y-Zplane.

FIGS. 5A to 5D illustrate light intensity distributions of thediffracted light.

FIG. 6 indicates a relationship between the diffraction efficiency andthe optical path length difference.

FIG. 7 illustrates the light intensity distribution of diffracted lightsin which the optical path length difference is provided.

FIGS. 8A to 8C illustrates the light intensity distribution ofdiffracted lights with respect to each wavelength corresponding to blue,green and red.

FIGS. 9A to 9C illustrate the configuration of the screen according tothe first modification.

FIGS. 10A to 10D illustrate a relationship between the configuration ofthe screen and the diffracted lights on the Y-Z plane.

FIGS. 11A and 11B illustrate a light intensity distribution of thediffracted lights according to the first modification.

FIGS. 12A and 12B illustrate a light intensity distribution of thediffracted lights according to the first modification.

FIG. 13 illustrates a light intensity distribution of the diffractedlights according to the first modification.

FIGS. 14A and 14B illustrate a light intensity distribution of thediffracted lights according to the first modification.

FIGS. 15A and 15B illustrate the configurations of the screens accordingto the second modification.

FIGS. 16A to 16C illustrate the configuration of the screen according tothe third modification.

FIGS. 17A to 17C illustrate the configuration of the screen according tothe fourth modification.

FIGS. 18A and 18B illustrate the configuration of the screen accordingto the fifth modification.

FIGS. 19A to 19C illustrate the configurations of the screens accordingto the seventh, eighth and ninth modifications.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

According to a preferable embodiment of the present invention, there isprovided a lens array including plural lenses configured to have thesame effective diameter and to have a structure that generates anoptical path length difference in transmission light or reflectivelight, wherein each of the plural lenses is arranged at an intervalbased on the effective diameter thereby to form a two-dimensional basicperiodic structure, wherein a part of the plural lenses form a basicblock which is a combination of lenses having the structure thatgenerates the optical path length difference, wherein the basic block isrepeatedly arranged to form a two-dimensional secondary periodicstructure whose period is longer than the period of the basic periodicstructure, and wherein the period of the secondary periodic structure isan integer multiple of the period of the basic periodic structure.

The lens array includes plural lenses configured to have the sameeffective diameter and to have a structure that generates an opticalpath length difference in transmission light or reflective light. Eachof the plural lenses is arranged at an interval based on the effectivediameter thereby to form a two-dimensional basic periodic structure.Some lenses of the plural lenses form a basic block which is acombination of lenses having the structure that generates the opticalpath length difference. The basic block is repeatedly arranged to form atwo-dimensional secondary periodic structure whose period is longer thanthe period of the basic periodic structure. The period of the secondaryperiodic structure is an integer multiple of the period of the basicperiodic structure.

By having the secondary periodic structure whose period is an integermultiple of the period of the basic periodic structure based on thearrangement of the lenses, the above lens array diffuses diffractedlights so that any clearance of the light intensity distribution at theview point is filled. Thus, in this mode, the lens array can suitablysuppress the irregular brightness while preventing the resolution fromdeteriorating due to the difference of effective diameters of thelenses.

In one mode of the lens array, the basic block is formed by the part ofthe plural lenses combined in a grid pattern and has a staggeredarrangement thereof with respect to each different structure. Accordingto this mode, the lens array can generate first order diffracted lightsin the diagonal direction of each 0th order diffracted light toeffectively fill the clearance of the light intensity distribution ofdiffracted lights. Thus, it is possible to suitably suppress theirregular brightness.

In another mode of the lens array, the period of the secondary periodicstructure is four times as long as the period of the basic periodicstructure. This mode enables the first order diffracted lights generatedthrough the secondary periodic structure not to overlap with each otherat the same position thereby to suppress the irregular brightness.

In still another mode of the lens array, the basic block is formed bythe part of the plural lenses combined in a grid pattern and configuredof a combination of at least three kinds of lenses which generates theoptical path length difference. Even in this mode, it is possible toform the secondary periodic structure whose period is an integermultiple of the period of the basic periodic structure based on thearrangement of the lenses.

In still another mode of the lens array, the plural lenses have the samecurvature and are arranged with a height difference to generate theoptical path length difference. The lenses of the lens array accordingto this mode can suitably generate the optical path length difference inthe transmission light.

In still another mode of the lens array, the optical path lengthdifference is determined to meet a condition that the diffractionefficiency of the 0th order diffracted light of the lens array issubstantially equal to the diffraction efficiency of the first orderdiffracted lights of the lens array. The lens array according to thismode can generate each 0th order diffracted light and its positive andnegative first order diffracted lights with the same intensity therebyto fill the clearance of the light intensity distribution at the viewpoint.

In still another mode of the lens array, the optical path lengthdifference is determined to meet a condition that the diffractionefficiency of the 0th order diffracted light of the light intensitydistributions substantially zero. The lens array according to this modeevenly fill the clearance of the light intensity distribution at theviewpoint by the positive and negative first order diffracted lights.

In still another mode of the lens array, the optical path lengthdifference is determined to be the shortest length or the secondshortest length out of lengths which meet the condition. The longer theoptical path length difference is, the larger the variation of thediffraction efficiency along with the variation of the wavelengthbecomes. The lens array according to this mode can suitably suppress theratio of the diffraction efficiency of diffracted light(s) per eachorder from highly depending on the wavelength even when the synthesizedlight with plural wavelengths enters the lens array.

In a preferable example of the lens array, the lens array is irradiatedby a laser light emitted by an image projection device equipped with atleast one laser light source.

In still another mode of the lens array, the optical path lengthdifference is determined based on the longest wavelength out of thewavelengths of laser lights emitted by the at least one laser lightsource. Generally, the longer the wavelength is, the longer the pitch ofthe diffracted light becomes. Thus, the lens array according to thismode can fill the clearance of the light intensity distribution at theview point regarding all wavelengths of light.

In still another mode of the lens array, the optical path lengthdifference is determined based on the wavelength with the highestluminous sensitivity out of the wavelengths of laser lights emitted bythe at least one laser light source. Even in this mode, the lens arraycan suitably suppress the irregular brightness.

In still another mode of the lens array, the optical path lengthdifference is determined based on a wavelength between the longestwavelength and the wavelength with the highest luminous sensitivity outof the wavelengths of laser lights emitted by the at least one laserlight source. Even in this mode, the lens array can suitably suppressthe irregular brightness.

In a preferable example of the lens array, the numerical apertures ofthe plural lenses are substantially equal.

In still another mode of the lens array, the plural lenses generate theoptical path length difference based on a curvature difference. Even inthis mode, the lens array can suitably generate the optical path lengthdifference in the transmission light.

In still another mode of the lens array, the plural lenses generate theoptical path length difference based on a difference of signs ofcurvatures thereof. Even in this mode, the lens array can suitablygenerate the optical path length difference in the transmission light.Preferably, the above lens array is mounted on an image projectiondevice.

In still another mode of the lens array, the lens array is a reflectivelens array with a lens array surface on which a reflection coating isapplied. Even in this mode, the lens array can suitably suppress theirregular brightness while preventing the resolution from deterioratingdue to the difference of effective diameters of the lenses thereof.

Embodiment

A preferred embodiment of the present invention will be explainedhereinafter with reference to the drawings.

[Configuration of Head-Up Display]

FIG. 1A illustrates schematic configuration of a head-up display whichis an example of the “image projection device” according to the presentinvention. The head-up display is a system which lets a person inside avehicle equipped with a windshield 25 and a dashboard 29 visuallyrecognize a virtual image, and includes a light source unit 1, a screen2, and a concave mirror 3.

The light source unit 1 includes laser devices corresponding to red (R),green (G) and blue (B), and scans the screen 2 through a MEMS mirror bysynthesized laser light modulated based on image signals.

The screen 2 enlarges the exit pupil by expanding the divergence angleof light emitted by the light source unit 1. The screen 2 is a microlensarray in which plural microlenses are arranged. The light emitted by thelight source unit 1 enters the concave mirror 3. As mentioned later, aphase structure whose period is larger than the period of themicrolenses is incorporated into the screen 2. Thereby, the screen 2simultaneously generates plural diffracted lights whose diffractionangles are each smaller than the diffraction angle of a diffracted lightgenerated by the microlens array. The screen 2 is an example of the“transparent substrate” according to the present invention. Hereinafter,the lateral direction of the intermediate image generated by the screen2 is defined as “X axis”, the longitudinal direction thereof is definedas “Y axis”, the direction perpendicular to an incident plane of thescreen 2 is defined as “Z axis”, and each positive direction thereof isdefined as illustrated in the drawings.

The concave mirror 3 reflects the laser light projected from the screen2 thereby to lead the light to the windshield 25. In this case, byreflecting the laser light, the concave mirror 3 enlarges the imagecorresponding to the laser light. The laser light reflected by theconcave mirror 3 is further reflected by the windshield 25 to reach theeyes of an observer. Thereby, the observer visually recognizes thevirtual image.

It is noted that the configuration of the head-up display illustrated inFIG. 1A is merely one example, and the configuration to which thepresent invention can be applied is not limited to the configuration.For example, in the case of the head-up display illustrated in FIG. 1B,the screen 2 includes reflective microlenses. Then, through thereflective microlenses, the head-up display may enlarge the pupil exitby expanding the divergence angle of the light emitted by the lightsource unit 1. In another example, the head-up display is equipped witha combiner between the windshield 25 and the eye point Pe and lets thecombiner reflect the laser light reflected by the concave mirror 3.Thereby, the head-up display leads the laser light of the light sourceunit 1 to the eye point Pe thereby to let the driver visually recognizethe virtual image.

[Screen]

(1) Schematic Configuration of Screen

FIG. 2 illustrates a side view of the screen 2 in the Y-Z plane. Asillustrated in FIG. 2, on the incident plane of the screen 2 on whichthe light of the light source unit 1 is incident, there is formed amicrolens array 20 in which the microlenses 21 (21H, 21L) with differentheights in the Z axis direction are alternatively arranged. Here, thetop position of an upper level microlens 21H is higher in the Z axisdirection than the top position of a lower level microlens 21L, andthere is formed a height difference between the upper level microlens21H and the neighboring lower level microlens 21L. It is noted that theeffective diameters and numerical apertures of all the microlenses 21are equal regardless of whether each of them is an upper level microlens21H or a lower level microlens 21L. As illustrated in FIG. 2, the period(referred to as “concave-and-convex period PC”) of a pair of a concaveand a convex formed by an upper level microlens 21H and a lower levelmicrolens 21L is twice, that is an integer multiple, as long as theperiod (referred to as “lens period PL”) of the microlenses 21.

FIG. 3A illustrates the height of the incident plane of the screen 2. InFIG. 3A, rectangle areas with notations “HIGH” correspond to upper levelmicrolenses 21H, and rectangle areas with notations “LOW” correspond tolower level microlenses 21L.

As illustrated in FIG. 3A, an upper level microlens 21H and a lowerlevel microlens 21L are alternatively arranged one by one in the X axisdirection and in the Y axis direction, and they are asymmetric withrespect to the X axis and the Y axis. A rectangle area (e.g., the areain the frame 70) where two upper level microlens 21H and two lower levelmicrolens 21L are arranged in zigzag (i.e., in a staggered arrangement)forms a unit structure (referred to as “basic block”) of the periodicalphase structure of the microlens array 20. Each of the microlenses 21functions as the “basic periodical structure” and the basic blockfunctions as the “secondary periodical structure” according to thepresent invention.

FIG. 3B illustrates an enlarged view of the basic block of the microlensarray 20 and FIG. 3C illustrates the height difference between a lowerlevel microlens 21L and an upper level microlens 21H in the Z axisdirection. As illustrated in FIG. 3B, the basic block is quartered in across shape, and diagonally-arranged areas have the same structure andareas adjacent to each other have different structures. In other words,the basic block is symmetric with respect to the center position andareas with the same structure are arranged in zigzag. Hereinafter, thewidth of the basic block in the X axis direction is referred to as “Px”,and the width thereof in the Y axis direction is referred to as “Py”. Inthis case, given that the diffraction order in the X axis direction isreferred to as “m” and that the diffraction order in the Y axisdirection is referred to as “n”, the diffraction angle “θx”, in the Xaxis direction, of the light which enters the basic block and which hasa wavelength “λ” is expressed through general optical calculations as

$\begin{matrix}{{{\sin\left( {\theta\; x} \right)} = \frac{m\;\lambda}{Px}},} & (1)\end{matrix}$and the diffraction angle “θy”, in the Y axis direction, of the lightwhich enters the basic block is expressed as

$\begin{matrix}{{\sin\left( {\theta\; y} \right)} = {\frac{n\;\lambda}{Py}.}} & (2)\end{matrix}$

Additionally, as illustrated in FIG. 3B, the height difference in the Zaxis direction between the lower level microlens 21L and the upper levelmicrolens 21H is referred to as “Δ”. Then, the optical path lengthdifference, which is caused by the height difference, between the lightpassing through the upper level microlens 21H and the light passingthrough the lower level microlens 21L is “Δ”, which is the same distanceas the height difference. Hereinafter, “Δ” is used as “height differenceΔ” or “optical path length difference Δ”.

(2) Examples of Light Intensity Distribution

Next, with reference to FIGS. 4A to 4E and FIGS. 5A to 5D, a descriptionwill be given of examples of light intensity distributions of diffractedlights generated by each microlens 21 of the screen 2.

FIG. 4A illustrates diffracted lights in the Y-Z plane on the assumptionthat the height reference Δ is not provided on the microlens array 20(i.e., only the lens array component is considered). FIG. 5A illustratesa light intensity distribution of the diffracted lights on a virtual X-Yplane (referred to as “standard plane Ptag”) which is away from thescreen 2 by substantially the same distance as the eye point Pe in thecase of FIG. 4A.

In this case, as illustrated in FIG. 5A, the diameter (referred to as“diffracted light size”) of each diffracted light on the standard planePtag is shorter than the pitch (referred to as “diffracted light pitch”)of each diffracted light on the standard plane Ptag, and therefore thereis clearance between diffracted lights adjacent to each other. Theclearance leads to irregular brightness. It is noted that, asillustrated in FIG. 5A, the diffracted light pitch in the diagonaldirection is larger than the diffracted light pitch in the X axisdirection and in the Y axis direction.

FIG. 4D illustrates the diffracted lights on the X-Z plane on theassumption that there is no height difference Δ on the microlens array20. The relationship between the pitch “P_(Lx)” of the microlenses 21 inthe X axis direction and the diffraction angle “θx” of the first orderdiffraction lights in the X axis direction is expressed as the followingequation.

$\begin{matrix}{{\sin\;\theta_{x}} = \frac{\lambda}{P_{Lx}}} & (3)\end{matrix}$

FIG. 4E illustrates the diffracted lights on the Y-Z plane on theassumption that there is no height difference Δ in the microlens array20. The relationship between the pitch “P_(Ly)” of the microlenses 21 inthe Y axis direction and the diffraction angle “θy” is expressed as thefollowing equation.

$\begin{matrix}{{\sin\;\theta_{y}} = \frac{\lambda}{P_{Ly}}} & (4)\end{matrix}$

Thus, the pitch “x” of the diffracted lights in the X axis direction ona virtual X-Y plane which is away from the microlens toward negative Zdirection by distance “d” is expressed by the following equation.x=d×sin θ_(x)   (5)Similarly, the pitch “y” of the diffracted lights in the Y axisdirection on a virtual X-Y plane which is away from the microlens towardnegative Z direction by distance “d” is expressed by the followingequation.y=d×sin θ_(y)   (6)

Furthermore, when the total angle of the converging angle of the lightconverging on the microlens array 20 from the light source unit 1 isreferred to as “2α”, the beam size “w” at the view point is expressed asthe following equation.w=2×d×sin α  (7)

It is noted that the total angle “2α” and the beam size “w” at the viewpoint may be calculated from the outline of the beam which can begeometrically calculated. In this case, if the light intensitydistribution of the laser beam is a Gaussian distribution and the fullwidth at half maximum of the light intensity distribution at the viewpoint is smaller than the outline of the beam which can be geometricallycalculated, the total angle “2α” of the converging angle may beconsidered as the total angle of the converging angle corresponding tothe full width at half maximum of the intensity distribution of thelaser beam and the beam size “w” may be also considered as the fullwidth at half maximum of the intensity distribution of the beam at theview point.

FIG. SD illustrates the light intensity distribution of the diffractedlights on the virtual X-Y plane which is away from the screen 2 by thedistance d in the case of FIG. 4D and FIG. 4E. With reference to FIG.5D, the peak of the pitch (interval) of the diffracted lights on thevirtual X-Y plane is the pitch between the diffracted lights diagonallyfacing each other, and the pitch “u” of the diffracted lights isexpressed as the following equation.u=√{square root over (x ² +y ²)}  (8)

In this case, the clearance “s” between the diffracted lights diagonallyfacing each other is expressed as the following equation by using “w”which indicates the beam size in the diagonal direction.s=u−w   (9)

Furthermore, given that “2α” indicates the total angle of the convergingangle of the laser beam in the diagonal direction and that the equations(3), (4), (5), (6) and (7) are substituted into the equation (9), themaximum clearance s of the diffracted lights is expressed as thefollowing equation.

$\begin{matrix}{s = {d \times \left\{ {\sqrt{\left( \frac{\lambda}{P_{Lx}} \right)^{2} + \left( \frac{\lambda}{P_{Ly}} \right)^{2}} - {2 \times \sin\;\alpha}} \right\}}} & (10)\end{matrix}$

When the above value meets the following conditions≥0   (11),i.e., when the following condition

$\begin{matrix}{{\sin\;\alpha} \leq {\frac{\lambda}{2\;}\sqrt{\left( \frac{1}{P_{Lx}} \right)^{2} + \left( \frac{1}{P_{Ly}} \right)^{2}}}} & (12)\end{matrix}$is satisfied, areas without any overlap with light occurs betweenneighboring diffracted lights on the virtual X-Y plane. This leads toserious irregular brightness. Namely, on the assumption that the heightdifference Δ is not provided on the microlens array 20, the irregularbrightness becomes serious when the converging angle α of the lightprojected from the light source unit 1 is small or when the pitch of themicrolenses 21 is small.

FIG. 4B illustrates the diffracted lights on the Y-Z plane in such acase that only the height difference component of the microlens array 20is considered. FIG. 5B illustrates the light intensity distribution ofthe diffracted lights on the standard plane Ptag in the case of FIG. 4B.In the case of the example illustrated in FIG. 4B and FIG. 5B, theheight difference (optical path length difference) Δ is set to“(N±0.283) λ” (“N” is an integer which is equal to or larger than 0).

In this case, as illustrated in FIG. 5B, the diffracted light (referredto as “0th order diffracted light”) whose order m and order n are both“0” and the diffracted lights (referred to as “first order diffractedlights”) whose order m and order n are both “±1” arise with the sameintensity, while any diffracted light (“even order diffracted light”)whose order m and/or order n is even other than 0 does not arise. Thehigher the order is, the lower the intensity of the diffracted lightbecomes. These theoretical grounds will be described in detail at thesection “(3) Analysis of Diffraction Efficiency”. Further, as describedlater, by adjusting the optical path length difference Δ, it is possibleto adjust the distribution of the diffraction efficiency of the 0thorder light and the first order lights.

FIG. 4C illustrates the diffracted lights on the Y-Z plane of themicrolens array 20 in such a case that the component indicated by FIG.4A and the component indicated by the FIG. 4B are combined. FIG. 5Cillustrates the light intensity distribution of the diffracted lights onthe standard plane Ptag in the case of FIG. 4C. For the sake ofvisibility, the 0th order diffracted lights in FIG. 5C are describeddarker than the first order diffracted lights.

As illustrated in FIG. 5C, in this case, on the standard plane Ptag, the0th order diffracted lights corresponding to the distribution of thediffracted lights illustrated in FIG. 5A are distributed while the firstorder diffracted lights are arranged in every four diagonal directionswith respect to each 0th order diffracted light. Namely, in this case,compared to the example of no height difference illustrated in FIG. 4Aand FIG. 5A, the first order diffracted lights are inserted into eachdiagonal clearance where the diffracted light pitch is at its maximum.Thus, in this case, it is possible to efficiently fill the clearancebetween the diffracted lights with a few diffracted lights.

Additionally, since the concave-and-convex period PC is determined to bean integer multiple (twice in this case) of the lens period PL, thediffracted lights are orderly arranged on the standard plane Ptag. Thus,the light intensity distribution at the view point comes close to aneven distribution. Generally, in such a case that plural periodicalstructures whose periods of periodical structures are different arecombined, moire fringes arises due to the difference of the periods.Additionally, even when periodical structures with the same period orwith integer multiple period are combined, a shift of the positionalrelationship leads to moire fringes. In contrast, according to theembodiment, since the concave-and-convex period PC which is an integermultiple of the lens period PL is incorporated, the unconformity betweenthe period of the individual microlens 21 and the incorporated integermultiple period thereof does not arise. Thus, according to embodiment,it is possible to prevent the occurrence of moire fringes.

(3) Analysis of Diffraction Efficiency

Next, a description will be given of the diffraction efficiency ofdiffracted lights on the screen 2. The diffraction efficiency “I(m, n)”of a transparent light with the wavelength λ passing through the phasestructure including basic block illustrated in FIG. 3B is expressed withreference to Px, Py, Δ illustrated in FIG. 3B as the following generalequation (13).

$\begin{matrix}{I_{m,n} = {{{\frac{1}{P_{x} \cdot P_{y}}{\int_{0}^{P_{x}}{\int_{0}^{P_{y}}{{A\ \left( {x,y} \right)}\exp{\left\{ {{i \cdot 2}{\pi \cdot {\phi\left( {x,y} \right)}}} \right\} \cdot \exp}\left\{ {{{- i} \cdot 2}{\pi\left( {{\frac{m}{P_{x}} \cdot x} + {\frac{n}{P_{y}} \cdot y}} \right)}} \right\}{dxdy}}}}}}2}} & (13)\end{matrix}$

Here, “A(x, y)” indicates an intensity distribution and “φ(x,y)”indicates a phase distribution (i.e., distribution of optical pathlength differences) in one period, and they are expressed as thefollowing equations (14) and (15).

$\begin{matrix}{{A\left( {x,y} \right)} = 1} & (14) \\{{\phi\left( {x,y} \right)} = \left\{ \begin{matrix}{0\mspace{14mu}\ldots\mspace{14mu}\left( {{{{0 \leq x < {0.5 \cdot P_{x}}}\&}\mspace{11mu} 0} \leq y < {0.5 \cdot P_{y}}} \right)} \\{\bigtriangleup\mspace{14mu}\ldots\mspace{14mu}\left( {{{{{0.5 \cdot P_{x}} \leq x < {1 \cdot P_{x}}}\&}\mspace{11mu} 0} \leq y < {0.5 \cdot P_{y}}} \right)} \\{0\mspace{14mu}\ldots\mspace{14mu}\left( {{{{0 \leq x < {0.5 \cdot P_{x}}}\&}\mspace{11mu}{0.5 \cdot P_{y}}} \leq y < {1 \cdot P_{y}}} \right)} \\{\bigtriangleup\mspace{14mu}\ldots\mspace{14mu}\left( {{{{{0.5 \cdot P_{x}} \leq x < {1 \cdot P_{x}}}\&}\mspace{11mu}{0.5 \cdot P_{y}}} \leq y < {1 \cdot P_{y}}} \right)}\end{matrix} \right.} & (15)\end{matrix}$

When A(x, y) indicated by the equation (14) and φ(x,y) indicated by theequation (15) are substituted into the diffraction efficiency I(m, n)indicated by the equation (13), the following equation (16) is obtained.

$\begin{matrix}{{I\left( {m,n} \right)} = {{{\frac{\sin\left( {\pi m} \right)}{\pi m}\frac{\sin\left( {\pi n} \right)}{\pi n}} - {\quad{{\frac{1}{2}\left\lbrack {1 - {\exp\left( {i\frac{2\pi}{\lambda}\Delta} \right)}} \right\rbrack}\left\{ {{\frac{\sin\left( {\pi m} \right)}{\pi m}\frac{\sin\left( {\pi n} \right)}{\pi n}} + {\frac{1 - {\cos\left( {\pi m} \right)}}{\pi m}\frac{1 - {\cos\left( {\pi n} \right)}}{\pi n}}} \right\}}}^{2}}}} & (16)\end{matrix}$

Regarding the equation (16), the values of the following member (twooccurences in the equation 16)

$\frac{\sin\left( {\pi m} \right)}{\pi m}\frac{\sin\left( {\pi n} \right)}{\pi n}$are “1” only when “m=0” and “n=0” are satisfied, and the values is “0”in the other cases. The values of the following member

$1 - {\exp\;\left( {i\frac{2\pi}{\lambda}\Delta} \right)}$vary from 0 to 1 with the period λ with respect to the light pathdifference Δ. The value of the following member

$1 - {\frac{\cos\left( {\pi m} \right)}{\pi\; m}1} - \frac{\cos\left( {\pi n} \right)}{\pi\; n}$is “0” if “m” and/or “n” are even, and the absolute value of the memberwith the above term decreases with increasing the absolute values of “m”and “n”.

The diffraction efficiency of the 0th order diffracted light is obtainedthrough substitutions of “m=0” and “n=0” into the equation (16) andexpressed as the following equation (17).

$\begin{matrix}{{I\left( {0,0} \right)} = {\frac{1}{2}\left\{ {1 + {\cos\left( {\frac{2\pi}{\lambda}\Delta} \right)}} \right\}}} & (17)\end{matrix}$

Similarly, the diffraction efficiency of the first order diffractedlight is obtained and expressed through substitutions of “m, n=±1” intothe equation (16) as the following equation (18).

$\begin{matrix}{{I\left( {{\pm 1},{\pm 1}} \right)} = {\frac{8}{\pi^{\dashv}}\left\{ {1 - {\cos\left( {\frac{2\pi}{\lambda}\Delta} \right)}} \right\}}} & (18)\end{matrix}$

Additionally, the equation (16) indicates that the diffractionefficiency of any even order diffracted light is “0”, and that thehigher the order of the diffracted light is, the smaller the diffractionefficiency of the diffracted light becomes.

FIG. 6 indicates the relationship between the diffraction efficiencycalculated through the equation (16) and the normalized optical pathlength difference which is the optical path length difference Δnormalized by being divided by λ. The graph “G0” indicates thediffraction efficiency of the 0th order diffracted light, the graph “G1”indicates the individual diffraction efficiency of the first orderdiffracted lights, the graph “G1A” indicates the sum of four diffractionefficiencies of the first order diffracted lights, and the graph “G01A”indicates the sum of the diffraction efficiency of the 0th orderdiffracted light and four diffraction efficiencies of the first orderdiffracted lights. As illustrated in FIG. 6, when the optical pathlength difference Δ is equal to “(N±0.283) λ” (see the condition [1]),the diffraction efficiency of each 0th order diffracted light and thetotal diffraction efficiency of four first order diffracted lights areequal to “0.3965”, respectively. The sum of these two diffractionefficiencies is “0.793” and remained minor diffraction efficiency isdistributed to higher order diffracted lights which is the third orderor an odd order larger than third order. In this case, as explained inFIGS. 4C and 5C, since the first order diffracted lights are irradiatedin the four diagonal directions of each 0th order diffracted light, itis possible to suitably fill the clearance between the diffractedlights.

If the optical path length difference Δ is equal to “(N±0.377) λ” (seethe condition [2]), the diffraction efficiency of the 0th orderdiffracted light and the individual diffraction efficiency of the firstorder diffracted light are equal to “0.141”, respectively. The sum ofthese diffraction efficiencies is “0.705” and remained minor diffractionefficiency is distributed to higher order diffracted lights which isthird order or an odd order larger than third order.

If the optical path length difference Δ is equal to “(N±0.5) λ” (see thecondition [3]), the diffraction efficiency of the 0th order diffractedlight is “0” and the individual diffraction efficiency of four firstorder diffracted lights is “0.164”. The total diffraction efficiency is“0.657” and remained minor diffraction efficiency is distributed tohigher order diffracted lights which is third order or an odd orderlarger than third order.

FIG. 7 illustrates the light intensity distribution of the diffractedlight on the standard plane Ptag in a case where the optical path lengthdifference Δ is “(N±0.5) λ”.

When the optical path length difference Δ is “(N±0.5) λ”, the intensityof the 0th order diffracted light becomes “0”. According to the exampleillustrated in FIG. 7, the standard plane Ptag is almost-evenly filledby the first order diffracted lights. Meanwhile, when theconcave-and-convex period PC is determined to be twice as long as thelens period PL, the diffracted light pitch generated through theconcave-and-convex period PC is one-half of the diffracted light pitchgenerated through the lens period PL. Thus, in this case, the firstorder diffracted lights generated through the concave-and-convex periodPC with respect to each diffracted light generated through the lensperiod PL overlap with each other. As a result, the number of diffractedlights in appearance is the same as the number in the case where noheight difference are provided and the diffracted light pitch is alsothe same as the diffracted light pitch in the case where no heightdifference are provided. Thus, this example is not preferable since theirregular brightness due to the clearance between diffracted lightscannot be suppressed. Accordingly, when the concave-and-convex period PCis determined to be twice as long as the lens period PL as with theembodiment, it is preferable to set the optical path length difference Δto “(N±0.283) λ” thereby to equalize the diffraction efficiency of the0th order light generated through the concave-and-convex period PC andthe total diffraction efficiency of different four first orderdiffracted light.

(4) Relationship between Wavelength and Phase Structure

Since the light source unit 1 emits lights with different wavelengthscorresponding to R, G and B, such a problem arises that whichwavelengths of R, G and B should be selected as the standard fordetermining the height difference Δ between the lower level microlens21L and the upper level microlens 21H. The description thereof will beexplained.

Generally, the longer the wavelength is, the larger the diffractionangle of the diffracted light generated on the microlens array 20becomes. Thus, the longer the wavelength is, the wider the diffractedlight pitch (see FIG. 5A) becomes. The size of the diffracted lightdepends on the numerical aperture and does not depend on the wavelength.As a result, the longer the wavelength of the light is, the wider thediffracted light pitch becomes.

FIG. 8A illustrates the light intensity distribution of the diffractedlights on the standard plane Ptag in the case of blue light (whosewavelength is 435.8 nm), and FIG. 8B illustrates the light intensitydistribution of the diffracted lights on the standard plane Ptag in thecase of green light (whose wavelength is 546.1 nm). FIG. 8C illustratesthe light intensity distribution of the diffracted lights on thestandard plane Ptag in the case of red light (whose wavelength is 700nm). As illustrated in FIGS. 8A to 8C, the diffracted light pitch in thecase of the blue light which has the shortest wavelength is the shortestpitch whereas the diffracted light pitch in the case of the red lightwhich has the longest wavelength is the longest pitch.

In consideration of above things, as a first preferable example, theheight difference Δ is determined in accordance with the wavelength(i.e., wavelength of red light) which produces the widest diffractedlight pitch. This makes it possible to prevent the occurrence ofclearance on the light intensity distribution of the diffracted lightsregarding each laser light of R, G and B thereby to preferably suppressthe irregular brightness.

In contrast, as a second preferable example, in such a case that thediffracted light pitch does not particularly depend on the wavelength,the height difference Δ may be determined in accordance with thewavelength (i.e., wavelength of green light) which produces the maximumluminous sensitivity. As a third preferable example, in consideration ofboth of the diffracted light pitch and the luminous sensitivity, theheight difference Δ may be determined in accordance with theintermediate wavelength between the longest wavelength and thewavelength corresponding to the maximum luminous sensitivity.

A description will be given of a method for determining the integer Nwhich defines the height difference (optical path length difference) Δ.The larger the integer N is, the larger the height difference Δ becomes.Besides, the definition of the diffraction efficiency expressed by theequation (16) indicates that the larger the height difference Δ is, themore the ratio between the 0th order diffracted light and the firstorder diffracted light with respect to each of R, G and B varies.Namely, the variation of the diffraction efficiency along with thevariation of the wavelength increases with increasing height differenceΔ. In consideration of above things, it is preferable to set the integerN to “0” or “1” and make the height difference Δ possibly short.

As described above, the microlens array 20 of the screen 2 according tothe embodiment includes upper-level microlenses 21H and lower-levelmicrolenses 21L which are formed on the incidence surface of the screen2, which have the same effective diameter, and which have a structurethat generates an optical path length difference Δ in transmissionlight. By disposing the upper-level microlenses 21H and the lower-levelmicrolenses 21L at an interval based on the effective diameter, thebasic periodic structure of a lens period PL is formed. Further, theupper-level microlens 21H and the lower-level microlens 21L form a basicblock including a combination of the lenses having a structure thatgenerates the optical path length difference. A concave-and-convexperiod PC based on the basic block is an integer multiple of the lensperiod PL. This configuration enables the microlens array 20 to suitablysuppress the irregular brightness while preventing deterioration of theresolution due to different effective diameters of lenses.

[Modification]

Hereinafter, a description will be given of preferred modifications ofthe embodiment. Each modification to be mentioned later can be appliedto the above-mentioned embodiment in combination.

(First Modification)

According to the front view of the screen 2 illustrated in FIG. 3A, alower level microlens 21L and an upper level microlens 21H arealternatively arranged one by one. Instead, a predetermined number oflower level microlenses 21L and upper level microlenses 21H may bealternatively arranged.

FIG. 9A illustrates a side view of the screen 2A on the X-Y planeaccording to the modification. FIG. 9B illustrates a front view of thescreen 2A wherein each upper level microlens 21H is indicated by “HIGH”and each lower level microlens 21L is indicated by “LOW”. FIG. 9Cillustrates a basic block of the microlens array 20 in the exampleillustrated in FIGS. 9A and 9B.

According to FIG. 9A, the upper level microlenses 21H and the lowerlevel microlenses 21L are arranged by a block which has two columns andtwo rows, and each block is arranged in zigzag. Furthermore, as with thebasic blocks of the embodiment, the basic blocks illustrated in FIG. 9Care asymmetric with respect to the X axis and the Y axis and symmetricwith respect to the center. The concave-and-convex period PC in thiscase is four multiple, that is an integer multiple, of the lens periodPL as illustrated in FIG. 9A. Thus, as with the screen 2, the screen 2Acan suitably generate each diffracted light whose diffraction angle issmaller than the diffraction angle of each diffracted light generated bythe microlens array 20.

Next, with reference to FIGS. 10A to 10D and FIGS. 11A and 11B, adescription will be given of reasons why the first modification ispreferable.

FIG. 10A illustrates diffracted lights on the Y-Z plane according to theembodiment, wherein the height differences on the microlens array 20 areprovided by using the concave-and-convex period PC which is twice aslong as the lens period PL. FIG. 11A indicates the light intensitydistribution of diffracted lights on the standard plane Ptag. In thiscase, the first order diffracted lights generated through theconcave-and-convex period PC are positioned in between diffracted lightswhich are generated through the lens period PL thereby to fill theclearance between the beams and reduce the irregular brightness. In thiscase, however, as illustrated in FIG. 11B, the first order diffractedlights generated through the concave-and-convex period PC correspondingto a diffracted light which is generated through the lens period PLoverlap with the first order diffracted lights corresponding to theneighboring diffracted light which is generated through the lens periodPL. Thus, the number of the diffracted lights is apparently reducedalthough four first order diffracted lights, (+1, +1) order light, (+1,−1) order light, (−1, −1) order light and (−1, +1) order light, shouldbe originally generated though the concave-and-convex period PC withrespect to each diffracted light generated through the lens period PL.This leads to reduction of such an effect that the light intensitydistribution on the standard plane Ptag evenly spreads by disposing thediffracted lights as many as possible. In order to prevent the firstorder diffracted lights generated through the concave-and-convex periodPC from overlapping with each other, it is preferable to make theconcave-and-convex period PC three times or larger than three time aslong as the lens period PL thereby to limit the diffraction angle ofeach first order diffracted light to at most one third of the angularinterval of diffracted lights generated through the lens period PL.

In consideration of these agendas, according to the first modification,the height difference is provided by using the concave-and-convex periodPC which is four times period of the lens period PL so that all possiblediffracted lights are arranged on the standard plane Ptag.

FIG. 10B illustrates diffracted lights on the Y-Z plane wherein theheight difference is provided by using the concave-and-convex period PCwhich is four times period of the lens period PL. FIG. 12A indicates thelight intensity distribution of the diffracted lights on the standardplane Ptag in the case of FIG. 10B. In this case, as illustrated in FIG.12B, it is possible to differentiate each position of the first orderdiffracted lights which are generated through the concave-and-convexperiod PC and which are generated from diffracted lights of the lensperiod PL lying next to each other. This case is preferable in that allpossible diffracted lights are arranged on the standard plane Ptag.

Here, a description will be given of the reason why it is preferable toprovide the concave-and-convex period PC which is four times period ofthe lens period PL. In order to reduce the irregular brightness, it isdesirable that the light intensities of all the first order lightsgenerated through the concave-and-convex period PC should be equal. Toachieve this, it is preferable that the area of the lower level partshould be the same size as the area of the higher level part. Here, ifthe concave-and-convex period PC is designed to be an odd multipleperiod of the concave-and-convex period PC, the height difference liesinside the lens surface as illustrated in FIG. 10C. A lens with a heightdifference is not preferable in that the difference of characteristics,which causes irregular brightness, between a lens with a heightdifference and a lens without any height difference is generated due tosagging of the height difference and manufacturing errors. In otherwords, the concave-and-convex period PC according to the firstmodification should be determined to be four times as long as the lensperiod PL in consideration of the above-mentioned necessary conditionsthat the concave-and-convex period PC should be an even times period ofthe lens period PL and that the concave-and-convex period PC should bethree times or larger than three times as long as the lens period PL asmentioned above. This enables the height difference not to lie insidethe lens surface while enabling the first order diffracted lightsgenerated through the concave-and-convex period PC and not to overlapwith each other at the same position. It is noted that theconcave-and-convex period PC determined to six multiple or eightmultiple of the lens period PL also produces a similar effect. In thiscase, however, as illustrated in FIG. 13, the first order diffractedlights generated due to the concave-and-convex period PC arise in such astate that they are adjacent to the diffracted light generated throughthe lens period PL. This leads to unevenness of the pitch of diffractedlights when whole diffracted lights are observed. Thus, preferably, theconcave-and-convex period PC is designed to be four times as long as thelens period PL. Additionally, it is desirable that the optical pathlength difference Δ generated through the height difference should bedetermined in accordance with the lens period PL and the convergingangle a of light projected from the light source unit 1.

In such a case that the lens period PL should be small and/or theconverging angle a of light projected from the light source unit 1should be relatively small, it is preferable for the optical path lengthdifference Δ generated through the height difference to be determined to“N±0.377λ” (see the condition [2] in FIG. 6). In this case, both of thediffraction efficiency of a 0th order diffracted light generated throughthe concave-and-convex period PC and each diffraction efficiency of thefirst order diffracted lights corresponding thereto are equal to“0.141”. Thus, this case is preferable in that all diffracted lightswith the same intensity can be possibly arranged by use of the 0th orderdiffracted light and the first order diffracted lights.

Furthermore, there are preferred examples in such a case that the lensperiod PL can be determined to be relatively large and/or that theconverging angle α of the light projected from the light source unit 1can be determined to be relatively large. For the sake of explanation,the origin O indicates the intersection of the X axis and the Y axis,and “R axis” indicates the direction of the (+1, +1) order light and the(−1, −1) order light with respect to the center of a 0th order lightgenerated through the concave-and-convex period PC, and the positivedirection of the R axis coincides with the direction of the (+1, +1)order light. Similarly, “S axis” indicates the direction of the (−1, +1)order light and the (+1, −1) order light and the positive direction ofthe S axis coincides with the direction of the (−1, +1) order light.FIG. 10D illustrates diffracted lights on the R-Z plane at the time whenthe converging angle a of the light source unit 1 is determined to berelatively large so that the maximum length of clearance betweendiffracted lights becomes zero, and FIG. 14A indicates the lightintensity distribution on the standard plane Ptag in the case of FIG.10(D).

FIG. 14B illustrates four first order diffracted lights generatedthrough the concave-and-convex period PC with respect to one diffractedlight generated through the lens period PL. According to FIG. 14A, inorder not to generate any clearance between four first order diffractedlights, the converging angle of the light source unit 1 is determined sothat the two first order diffracted lights arranged in the R axisdirection are adjacent to each other and the two first order diffractedlights arranged in the S axis direction are adjacent to each other.Through the configuration designed as mentioned above, it is possible toeliminate non-irradiated areas on the standard plane Ptag.

As illustrated in FIG. 14B, since the width of a plurality of beamsformed by four first order diffracted lights in the R axis or in the Saxis direction is just twice the size of the diffracted light generatedthrough the lens period PL, it can be seen that the relationshipindicated by the following equation (19) is satisfied.

$\begin{matrix}{{\sin\;\alpha} = {\frac{\lambda}{4\;}\sqrt{\left( \frac{1}{P_{Lx}} \right)^{2} + \left( \frac{1}{P_{Ly}} \right)^{2}}}} & (19)\end{matrix}$

In this case, the optical path length difference Δ generated through theheight difference is set to “N±0.5λ” (see the condition [3] in FIG. 6)so that the diffraction efficiency of the 0th order diffracted lightgenerated through the concave-and-convex period PC becomes zero and thatthe 0th order diffracted light is therefore eliminated as illustrated inFIGS. 14A and 14B. This case is more preferable since the first orderdiffracted lights are evenly arranged and that non-irradiated areas areeliminated.

The above explanation is true of such a case that a phase structure isincorporated by any means other than making any height difference.

(Second Modification)

The microlenses 21 is determined to have two levels of height in the Zaxis. Instead, the microlenses 21 may be determined to have three ormore than three level of height in the Z axis.

FIG. 15A illustrates a basic block in a case where the height of themicrolenses 21 in the Z axis is determined to have three levels. In FIG.15A, each area with a notation “HIGH” indicates a microlens 21 with thehighest level of height in the Z axis direction, and each area with anotation “LOW” indicates a microlens 21 with the lowest level of heightin the Z axis direction and each area with a notation “MIDLLE” indicatesa microlens 21 with the secondary highest (i.e., secondary lowest) levelof height in the Z axis direction. According to this basic block, theconcave-and-convex period PC is three times, that is an integermultiple, as long as the lens period PL. Thus, at the time of having thebasic block illustrated in FIG. 15A, the screen 2 can also suitablyproduce each diffracted light whose diffraction angle is smaller thanthe diffraction angle of each diffracted light generated by themicrolens array 20.

FIG. 15B illustrates an example of a basic block in a case where themicrolenses 21 are designed to have five levels of height in the Z axis.In FIG. 15B, the height of each microlens 21 in the Z axis is indicatedby any one of “1” to “5”. According to this basic block, theconcave-and-convex period PC is five times, that is an integer multiple,as long as the lens period PL. Thus, even at the time of having thebasic block illustrated in FIG. 15B, the screen 2 can suitably produceeach diffracted light whose diffraction angle is smaller than thediffraction angle of each diffracted light generated by the microlensarray 20.

(Third Modification)

Instead of providing the concave-and-convex period PC which is aninteger multiple of the lens period PL through the height difference ofthe microlenses 21, the concave-and-convex period PC which is an integermultiple of the lens period PL may be provided through the difference ofthe curvature radii of the microlenses 21.

FIG. 16A illustrates a side view of the screen 2B according to the thirdmodification on the X-Y plane. As illustrated in FIG. 16A, in thisexample, the microlens array 20B on which microlenses 21Ba with a highcurvature radius and microlenses 21Bb with a low curvature radius arealternatively arranged is formed on the incident surface of the screen2B, wherein the effective diameters of the microlenses 21Ba and themicrolenses 21Bb are equal. The top position of the microlenses 21Bb ishigher than the top position of the microlenses 21Ba. In this case, theconcave-and-convex period PC based on the microlenses 21Bb and themicrolenses 21Ba is twice as long as the lens period PL.

FIG. 16B illustrates a front view of the screen 2B given that eachmicrolens 21Ba is expressed by “LARGE” and that each microlens 21Bb isexpressed by “SMALL”. FIG. 16C illustrates the basic block of themicrolens array 20B. As illustrated in FIGS. 16B and 16C, in this case,the microlenses 21Ba and the microlenses 21Bb are asymmetricallyarranged with respect to each of the X axis and the Y axis. Each basicblock is, in the same way as the embodiment, quartered in a cross shapeso that diagonally-arranged areas have the same structure and areasadjacent to each other have different structures.

As described above, by forming the concave-and-convex period PC which isan integer multiple of the lens period PL through the microlenses 21Baand the microlenses 21Bb with different radii, the screen can suitablygenerate each diffracted light whose diffraction angle is smaller thanthe diffraction angle of each diffracted light generated by themicrolens array 20. Additionally, according to the example in FIGS. 16Ato 16C, since any height difference is not provided, it is possible tosuitably suppress the loss of the light intensity and the deteriorationof the contrast caused by light scatters due to the height difference.

(Fourth Modification)

Instead of the height difference being provided, concave lenses andconvex lenses with different signs of curvature may be provided on themicrolens array 20 as the microlenses 21 thereof.

FIG. 17A illustrates a side view of the screen 2C according to the thirdmodification on the X-Y plane. As illustrated in FIG. 17A, in this case,the microlens array 20C on which the microlenses (convex lenses) 21Caand the microlenses (concave lenses) 21Cb are alternatively arranged isformed on the incident surface of the screen 2C, wherein the effectivediameters of the microlenses 21Ca and the microlenses 21Cb are equal.The top position of the microlenses 21Cb is lower in the Z axisdirection than the top position of the microlenses 21Ca. In this case,the concave-and-convex period PC based on the microlenses 21Cb and themicrolenses 21Ca is twice as long as the lens period PL.

FIG. 17B illustrates a front view of a basic block of the screen 2Cgiven that each microlens 21Ca is expressed by “

” and that each microlens 21Cb is expressed by “

”. FIG. 17C illustrates another basic block of the microlens array 20C.As illustrated in FIGS. 17B and 17C, in this case, the microlenses 21Caand the microlenses 21Cb are arranged in a staggered arrangement. Eachbasic block is, in the same way as the embodiment, quartered in a crossshape so that diagonally-arranged areas have the same structures andareas adjacent to each other have different structures.

According to the example illustrated in FIGS. 17A to 17C, the convexlenses 21Ca and the concave lenses 21Cb are arranged in a staggeredarrangement to form the concave-and-convex period PC that is an integermultiple of the lens period PL. Even in this case, the screen 2 cansuitably produce each diffracted light whose diffraction angle issmaller than the diffraction angle of each diffracted light generated bythe microlens array 20. Additionally, since the microlens array 20Caccording to FIGS. 17A to 17C has no height difference, the loss of thelight intensity due to any height difference can be suitably suppressed.

(Fifth Modification)

Plural different phase structures each of which has an integer multipleperiod of the lens period PL may be incorporated into the microlensarray 20.

FIG. 18A illustrates a front view of the microlens array 20D into whichthe twofold phase structures generated through height differences areincorporated. FIG. 18B illustrates the basic block of the microlensarray 20D. According to FIGS. 18A and 18B, the basic block of themicrolens array 20D has such a phase structure that rectangle areas(referred to as “intermediate blocks”) each of which includes fourmicrolenses 21 arranged by two columns and two rows are further arrangedby two columns and two rows. Here, each intermediate block is classifiedinto two categories based on the average height of each microlenses 21in the intermediate block. In FIGS. 18A and 18B, each intermediate blockwhose average height is high is labeled on its center as “HIGH” and theother intermediate blocks are each labeled on its center as “LOW”. Eachintermediate block is, in the same way as each basic block in theembodiment, quartered in a cross shape so that diagonally-arranged areashave the same structures and areas adjacent to each other have differentstructures. When a block composed of four intermediate blocks is deemedas one basic block, each basic block is also quartered in a cross shapeso that diagonally-arranged areas have the same structures and areasadjacent to each other have different structures.

In such a configuration, the phase structure of the intermediate blocksdivides incident light on the microlens array 20D into a 0th orderdiffracted light and first order diffracted lights whereas the phasestructure of the basic blocks further divides each of these diffractedlights into a 0th order diffracted light and first order diffractedlights. Thus, in this case, even if the pitch of the diffracted lightswithout consideration of the intermediate blocks and the basic blocks islarge, it is possible to suitably fill the clearance of the lightintensity distribution of diffracted lights on the standard plane Ptagby generating diffracted lights based on the intermediate blocks and thebasic blocks.

It is noted that such an intermediate block and a basic block asmentioned above may be formed based only on the height differencestructure of the microlenses 21 or formed based on difference ofcurvature radii according to the third modification or the fourthmodification.

(Sixth Modification)

Instead of being formed on the incident surface of the screen 2, themicrolens array 20 may be formed on the surface opposite to the incidentsurface of the screen 2 or may be formed on the both sides of the screen2.

(Seventh Modification)

The microlens array 20 may be a reflect-type lens array as illustratedin FIG. 19A, wherein the reflection coating is applied to the surface ofthe microlens array 20 opposite to the lens array surface.

(Eighth Modification)

In such a configuration according to the seventh modification, the lightpasses through the lens surface twice. Additionally, when it is areflective lens array and a light is diagonally incident to the lenses,the difference occurs between the position on the lens surface which thelight firstly passes through and the position on the lens surface whichthe light after the reflection passes through. This case is notpreferable in that moire fringes arise as with the case where the lightpasses through two microlens arrays with a position gap. Thus, themicrolens array 20 according to the eighth modification, as illustratedin FIG. 19B, is configured to have the lens array surface to which thereflection coating is applied and the opposite surface to which theantireflection coating is applied. In this case, since the light isreflected by the lens surface itself, the light receives the periodicalphase modulation of the lens array only once as with the case of thetransparent type lens array. This leads to a preferable result since themoire fringes which cause a problem in the seventh modification can besuppressed. In such a configuration according to the eighthmodification, stains adhered to the exposed lens surface do not affectthe light whereas it is difficult to remove the stains adhered to a lenssurface with a concave and convex shape. Thus, the above configurationis preferable in that image degradation due to stains can be suppressed.

(Ninth Modification)

As illustrated in FIG. 19C, the reflection coating is applied on thelens surface of the microlens array 20 according to the ninthmodification and the lens surface is directed to the light side. In sucha configuration, the light does not pass through the inside of the lenssurface, which suitably suppresses the loss of the light intensity dueto absorption by the material as well as the image deterioration due tobirefringence of the material and the irregular transmittance.Furthermore, the configuration does not need any antireflection coatingon the opposite side of the surface, which preferably reduces thecomponent cost. Since this opposite side of the surface does not affectthe performance of the lens array, it does not need a high surfaceaccuracy which is needed for a general optical element. This suitablymoderates the difficulty of component manufacturing. Furthermore, sincethis configuration have a high flexibility regarding the shape, thelayout in accordance with the shapes of peripheral components can bepossible. This suitably leads to a high flexibility of designing theshapes of the components.

For example, the microlens array 20 according to the sixth to ninthmodifications can be used as the screen 2 of the head-up displayillustrated in FIG. 1B.

DESCRIPTION OF REFERENCE NUMBERS

1 Light source unit

2 Screen

3 Concave mirror

20, 20A to 20D Microlens array

21 Microlens

What is claimed is:
 1. A lens array comprising: lenses arranged to forma first periodic structure, such that plural sets of the lenses arecombined to form respective blocks each having a structure that isconfigured to provide an optical path length difference in response to areceived laser light, wherein each of the blocks is arranged regularlyand repeatedly, wherein the lenses provide the optical path lengthdifference based on a curvature difference between ones of the lenses,and wherein a diffraction condition comprises a diffraction efficiencyof a 0th order diffracted light of the lens array being substantiallyequal to a sum of four diffraction efficiencies of a first orderdiffracted light of the lens array.
 2. The lens array according to claim1, wherein each of the blocks includes first lenses and second lensescombined in a grid pattern, and the first lenses have a staggeredarrangement with respect to the second lenses.
 3. The lens arrayaccording to claim 1, wherein the blocks form a second periodicstructure having a period longer than a period of the first periodicstructure, and wherein the period of the second periodic structure isfour times as long as the period of the first periodic structure.
 4. Thelens array according to claim 1, wherein each of the blocks is formed bya part of the lenses that are combined in a grid pattern and include atleast three kinds of lenses, to provide the optical path lengthdifference.
 5. An image projection device comprising the lens arrayaccording to claim 1, wherein the image projection device comprises atleast one laser light source that is configured to emit the laser light.6. A lens array comprising: lenses arranged to form a first periodicstructure, such that plural sets of the lenses are combined to formrespective blocks each having a structure that is configured to providean optical path length difference in response to a received laser light,wherein each of the blocks is arranged regularly and repeatedly, whereinthe lenses provide the optical path length difference based on acurvature difference between ones of the lenses and diffract thereceived laser light at a plurality of diffraction angles, and wherein adiffraction condition comprises a diffraction efficiency of a 0th orderdiffracted light of the lens array being substantially zero for all ofthe plurality of diffraction angles.
 7. An image projection devicecomprising the lens array according to claim 6, wherein the imageprojection device comprises at least one laser light source that isconfigured to emit the laser light.